{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"08_PT_Logistic_Regression","provenance":[{"file_id":"https://github.com/madewithml/basics/blob/master/notebooks/08_Logistic_Regression.ipynb","timestamp":1582817842854}],"collapsed_sections":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"markdown","metadata":{"id":"QsUcHSE0TcRM","colab_type":"text"},"source":["# Logistic Regression\n","\n","In this lesson, we're going to implement logistic regression for a classification task where we want to probabilistically determine the outcome for a given set of inputs. We will understand the basic math behind it, implement it in just NumPy and then in PyTorch."]},{"cell_type":"markdown","metadata":{"id":"G-CQd9joTxwB","colab_type":"text"},"source":["<div align=\"left\">\n","<a href=\"https://github.com/madewithml/basics/blob/master/notebooks/08_Logistic_Regression/08_PT_Logistic_Regression.ipynb\" role=\"button\"><img class=\"notebook-badge-image\" src=\"https://img.shields.io/static/v1?label=&amp;message=View%20On%20GitHub&amp;color=586069&amp;logo=github&amp;labelColor=2f363d\"></a>&nbsp;\n","<a href=\"https://colab.research.google.com/github/madewithml/basics/blob/master/notebooks/08_Logistic_Regression/08_PT_Logistic_Regression.ipynb\"><img class=\"notebook-badge-image\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"></a>\n","</div>"]},{"cell_type":"markdown","metadata":{"id":"VoMq0eFRvugb","colab_type":"text"},"source":["# Overview"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"orlWnRz2-wyO"},"source":["Logistic regression is just an extension on linear regression (both are generalized linear methods). We will still learn to model a line (plane) that models $y$ given $X$. Except now we are dealing with classification problems as opposed to regression problems so we want classification probabilities. We'll be using the softmax operation to normalize our logits ($XW$) to derive probabilities.\n","\n","Our goal is to learn a logistic model $\\hat{y}$ that models $y$ given $X$. \n","\n","$ \\hat{y} = \\frac{e^{XW_y}}{\\sum_j e^{XW}} $ \n","* $\\hat{y}$ = prediction | $\\in \\mathbb{R}^{NX1}$ ($N$ is the number of samples)\n","* $X$ = inputs | $\\in \\mathbb{R}^{NXD}$ ($D$ is the number of features)\n","* $W$ = weights | $\\in \\mathbb{R}^{DXC}$ ($C$ is the number of classes)\n","\n","This function is known as the multinomial logistic regression or the softmax classifier. The softmax classifier will use the linear equation ($z=XW$) and normalize it (using the softmax function) to produce the probabiltiy for class y given the inputs.\n","\n","**NOTE**: We'll leave the bias weights out for now to avoid complicating the backpropagation calculation."]},{"cell_type":"markdown","metadata":{"id":"T4Y55tpzIjOa","colab_type":"text"},"source":["* **Objective:**  Predict the probability of class $y$ given the inputs $X$. The softmax classifier normalizes the linear outputs to determine class probabilities. \n","* **Advantages:**\n","  * Can predict class probabilities given a set on inputs.\n","* **Disadvantages:**\n","  * Sensitive to outliers since objective is to minimize cross entropy loss. Support vector machines ([SVMs](https://towardsdatascience.com/support-vector-machine-vs-logistic-regression-94cc2975433f)) are a good alternative to counter outliers.\n","* **Miscellaneous:** Softmax classifier is going to used widely in neural network architectures as the last layer since it produces class probabilities."]},{"cell_type":"markdown","metadata":{"id":"3SYAo2FHl1I3","colab_type":"text"},"source":["# Data"]},{"cell_type":"markdown","metadata":{"id":"00B5uEM8Tb0d","colab_type":"text"},"source":["## Load data"]},{"cell_type":"markdown","metadata":{"id":"sYNIM3PxQGgo","colab_type":"text"},"source":["We'll used some synthesized data to train our models on. The task is to determine whether a tumor will be benign (harmless) or malignant (harmful) based on leukocyte (white blood cells) count and blood pressure. Note that this is a synethic dataset that has no clinical relevance."]},{"cell_type":"code","metadata":{"id":"A8rspXhNEgrL","colab_type":"code","colab":{}},"source":["import matplotlib.pyplot as plt\n","import numpy as np\n","import pandas as pd\n","from pandas.plotting import scatter_matrix\n","import urllib"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"zbcxlUHbT2z0","colab_type":"code","colab":{}},"source":["SEED = 1234\n","DATA_FILE = 'tumors.csv'"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"nchxHc9sX6UJ","colab_type":"code","colab":{}},"source":["# Set seed for reproducibility\n","np.random.seed(SEED)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"7sp_tSyItf1_","colab_type":"code","colab":{}},"source":["# Download data from GitHub to this notebook's local drive\n","url = \"https://raw.githubusercontent.com/madewithml/basics/master/data/tumors.csv\"\n","response = urllib.request.urlopen(url)\n","html = response.read()\n","with open(DATA_FILE, 'wb') as fp:\n","    fp.write(html)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"7alqmyzXtgE8","colab_type":"code","outputId":"8c2f91f2-9c4f-480f-f884-bbf45b06b6e7","executionInfo":{"status":"ok","timestamp":1583943593350,"user_tz":420,"elapsed":2716,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":204}},"source":["# Read from CSV to Pandas DataFrame\n","df = pd.read_csv(DATA_FILE, header=0)\n","df.head()"],"execution_count":84,"outputs":[{"output_type":"execute_result","data":{"text/html":["<div>\n","<style scoped>\n","    .dataframe tbody tr th:only-of-type {\n","        vertical-align: middle;\n","    }\n","\n","    .dataframe tbody tr th {\n","        vertical-align: top;\n","    }\n","\n","    .dataframe thead th {\n","        text-align: right;\n","    }\n","</style>\n","<table border=\"1\" class=\"dataframe\">\n","  <thead>\n","    <tr style=\"text-align: right;\">\n","      <th></th>\n","      <th>leukocyte_count</th>\n","      <th>blood_pressure</th>\n","      <th>tumor_class</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>13.472969</td>\n","      <td>15.250393</td>\n","      <td>malignant</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>10.805510</td>\n","      <td>14.109676</td>\n","      <td>malignant</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>13.834053</td>\n","      <td>15.793920</td>\n","      <td>malignant</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>9.572811</td>\n","      <td>17.873286</td>\n","      <td>malignant</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>7.633667</td>\n","      <td>16.598559</td>\n","      <td>malignant</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>"],"text/plain":["   leukocyte_count  blood_pressure tumor_class\n","0        13.472969       15.250393   malignant\n","1        10.805510       14.109676   malignant\n","2        13.834053       15.793920   malignant\n","3         9.572811       17.873286   malignant\n","4         7.633667       16.598559   malignant"]},"metadata":{"tags":[]},"execution_count":84}]},{"cell_type":"code","metadata":{"id":"3aqJxfKmnYTs","colab_type":"code","colab":{}},"source":["# Define X and y\n","X = df[['leukocyte_count', 'blood_pressure']].values\n","y = df['tumor_class'].values"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"lpoF3_EgDtPl","colab_type":"code","outputId":"72e26ec7-3627-4147-f289-db5b52bd600e","executionInfo":{"status":"ok","timestamp":1583943593618,"user_tz":420,"elapsed":2927,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":279}},"source":["# Plot data\n","colors = {'benign': 'red', 'malignant': 'blue'}\n","plt.scatter(X[:, 0], X[:, 1], c=[colors[_y] for _y in y], s=25, edgecolors='k')\n","plt.xlabel('leukocyte count')\n","plt.ylabel('blood pressure')\n","plt.legend(['malignant ', 'benign'], loc=\"upper right\")\n","plt.show()"],"execution_count":86,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAX4AAAEGCAYAAABiq/5QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0\ndHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nOydd3gUVRfG39m+M7ubHpIQkgBJCCGE\n0CJVuoB0pEkXpKoovYgfgiIqIkhHqYJUQbqC9CpNQJAuHSIQSoAUSLLv98dMwqYSIDSZ3/PsAztz\ny5mZ7Ll3zj3nXIEkVFRUVFReHTTPWwAVFRUVlWeLqvhVVFRUXjFUxa+ioqLyiqEqfhUVFZVXDFXx\nq6ioqLxi6J63ADnB3d2dAQEBz1sMFRUVlZeKffv2RZP0SH/8pVD8AQEB2Lt37/MWQ0VFReWlQhCE\nc5kdV009KioqKq8YquJXUVFRecVQFb+KiorKK8ZLYeNXUVF5eUlMTMTFixeRkJDwvEX5z2IymeDr\n6wu9Xp+j8qriV1FReapcvHgRVqsVAQEBEATheYvzn4Mkrl+/josXLyJ//vw5qqMqfhUVlVznwoUL\nWLNmDTw9PREYGKgq/aeIIAhwc3PDtWvXclxHtfGr/CeIjY3Fli1bcPr06ectyivP7Nk/ITi4GD76\naBNatx6Jy5ejkJSU9LzF+k/zqIOqqvhVXnqWL1+BPHn8Ua9eP4SFlcVbb7XJVUVz/fp13L17N9fa\n+y8TGxuLrl17ICFhC2Jj5+DOna1ISjIiKurf5y2aigOq4ld5qblz5w7efrsdYmNX4/btPxAffxa/\n/XYeU6dOe+K2z507h5IlK8HHJz/c3X3QocN7SExMzAWp/7scPXoUOl0+AGEORyXcvh37vER6YjZt\n2oS6desCAJYvX44vv/zymfV94MABrF69OtfbVRW/ygvLzz//jEqV6qFKlfpYunRppmV27twJna4o\ngEjliBlxcd2waNFvT9x/3botcOBADdy/fwP37p3F/Pkn8NVX3zxxu/9l8ufPj/v3zwG44nD0HkTR\nlOM27HY79uzZgz179sBut+e6jE9C/fr1MWDAgGfWn6r4VV4pRo8eh3btBmPLllbYtKkFWrXqi0mT\nvs9QzsfHB0lJZwA8mIlrtScQEODzRP1fuHABp06dgt0+ELIPhCvi44dixoyFT9Tufx03Nzf07t0T\nklQewAgYjV0hCLfh4+OVo/rnzp1DwYLhqFq1LapWbYvAwGI4dy7TrAM55uzZswgJCUH79u0RHByM\nVq1aYd26dShfvjyCgoKwe/duAMDu3btRtmxZFC9eHOXKlcPx48cztDVz5ky8//77AIB//vkHZcqU\nQdGiRTF48GBYLBYA8htC5cqV0aRJE4SEhKBVq1ZI2elw2LBhKF26NMLCwtC5c+fU45UrV0b//v0R\nGRmJ4OBgbN26Fffv38f//vc/LFiwABEREViwYMET3Yc0kHzhPyVLlqTKq4WLiw+BvwhQ+eyhp2f+\nTMtWrVqPZvObBJZRo/mCFosHjx49+kT9X7t2jUajE4FYBxlWsWjR8k/U7qvCunXr2L37Rxw2bDgP\nHTqU43qVK9elRvMZATsBO7Xaz1i5ct0nkuXMmTPUarX866+/mJyczBIlSvCdd96h3W7n0qVL2aBB\nA5JkTEwMExMTSZK///47GzduTJLcuHEj69SpQ5KcMWMG33vvPZJknTp1OHfuXJLkpEmTKElSanmb\nzcYLFy4wOTmZZcqU4datW0mS169fT5WrdevWXL58OUmyUqVK7NWrF0ly1apVrFatWob+HsaRI0cy\nHAOwl5noVHXGr/LCQRIxMVcAFHQ4WhA3bkRlWn7VqoUYOrQqypSZiBYtTmPXrk0ICQl5Ihnc3d3x\nxhu1YTS2BXAIwHqI4kfo37/7E7X7qlCtWjVMmDAan3wyCFqtNsf1tmz5DXb7RwAEAAKSkz/Cli1P\nbrbLnz8/ihYtCo1GgyJFiqBatWoQBAFFixbF2bNnAQAxMTFo2rQpwsLC0LNnT/z999/Ztrlz5040\nbdoUANCyZcs05yIjI+Hr6wuNRoOIiIjUPjZu3IjXXnsNRYsWxYYNG9L00bhxYwBAyZIlU8s/LVTF\nr/LCIQgCKlSoCa12FAACILTaUahW7c1My5tMJvTt2xs7d/6Gn376AaGhobkix/z509ClSwHkydMI\ngYH9MGHCYLRq1fLhFVUeG1dXHwAnHI4ch6tr3idu12g0pv5fo9GkftdoNKkeYJ988gmqVKmCw4cP\nY8WKFU8UaezYn1arRVJSEhISEtC9e3f8/PPPOHToEDp16pSmj5Q6KeWfJqriV3khmT17EgICfobF\nUggWSxACA3/FtGljn6kMoijiu+++xr//nsLJk/vQvn3bZ9r/q8iwYR9DFJsBmAVgFkSxOT777ONn\n0ndMTAzy5pUHmZkzZz60fJkyZbB48WIAwPz58x9aPkXJu7u74+7du/j5558fWsdqteLOnTsPLfeo\nqIpf5YXEz88PJ08ewJYtC7Bt22IcPbo39Uep8t+lW7fOmD9/NGrUWI4aNZZj/vzR6Nq10zPpu1+/\nfhg4cCCKFy+eoxn3mDFj8O233yI8PBynTp2Ck5NTtuWdnZ3RqVMnhIWFoWbNmihduvRD+6hSpQqO\nHDmS64u7ApVV5dxGEITpAOoCuEoyTDkWAWAyABOAJADdSe5+WFulSpWiuhHLi4fdbsfixYuxcuV6\nBAcHoHPnjvDwyLDZj8oLAElER0fDarXCZMq5a2VucPToURQuXPiZ9vksiIuLg9lshiAImD9/PubN\nm4dly5Y9N3kyu8+CIOwjWSp92ac5458JoFa6Y18DGEoyAsD/lO8qLymtWr2Ld975Cj/+GIrPPz+F\n0NBSiIrKfAFW5flx6NAhFCpUEr6+QXB19caAAUPwtCZ8rxL79u1DREQEwsPDMXHiRIwaNep5i5Rj\nnlqSNpJbBEEISH8YgE35vxOAy0+rf5Wny7Fjx7Bs2W+Ijz8FQERCAmC3f4DRo8fj66+HP2/xVBSS\nkpJQvXp9XL36MYAOAKIwfnxdFCkSiDZt2jxv8V5qKlasiIMHDz5vMR6LZ23j/wjASEEQLgD4BsDA\nZ9y/Si5x4sQJ6PURAMTUY/fvl8N3301D584f4NatW89POJVU9u7di/h4G4B3If/c8yI2dgCmTn22\ngWjqG8bT5VHv77NW/N0A9CSZD0BPAFkmVBEEobMgCHsFQdj7KOlGVXKf+/fvY+rUqWjcuC0GD/4U\n//77LyIjI3H//k4A55VSdgCzcf9+e8yaFYvatZs8R4lVUhBFEXb7bcjPJ4UYWK3SM5PBZDLh+vXr\nqvJ/SlDJx/8oazdPbXEXABRTz0qHxd0YAM4kKch5RGNI2rJpAoC6uPs8IYk33miEHTtiEBfXBkbj\nXlitK3Ho0G7Mm7cIgwZ9isTESkhOPgLAG8BqAAaYzX7Yv38DChUq9JyvIHex2+0QBOG55ZZPTEzE\nvHnz8Pvv2xEeHoxOnTrC2dk5y/IkUaJERfz9d1EkJn4E4CREsQtWrpyDKlWqPDOZ1R24ni5Z7cCV\n1eLuU021ACAAwGGH70cBVFb+Xw3Avpy0o6ZseH7s2bOHklSAwP3U1AVGY1cOHvwpSTkcPn/+IgRS\nwuzlMhZLCPfu3fucpc89rly5wlq13qJWq6ckufLjj4cyOTn5mcpgt9tZrVo9SlJFAuNpNrekr28w\nb968mW296Ohotm3bhe7u/ixSpCyXLVv2jCRWed4gi5QNT1PpzwMQBTl71kUAHQFUALAPwEEAuwCU\nzElbquJ/fixYsIBWa0OHfDUk8AMbN26bWmbKlO8pipEE/iWQTGAKvb0LMikp6TlKnrtERlalTteT\nwG0C/1AUI/ndd+OeqQzbtm2jJAWnGYTN5rc5cuSoZyqHystDVor/aXr1vJ3FqZJPq0+V3KdcuXJI\nTOwK4BwAfwD3IUmzUadOu9Qy777bEX//fQpTpgQD0MLPLwC//LLskXK0vMhcunQJf/11EElJayA7\nwlkRFzcCEycOQI8e7z8zOU6cOAGgNIAHr/Px8WVx6FD2OWVUVNKjRu6qZIuvry9GjBgGozECVmtD\nSFIhVKzonsYVUKPR4LvvvsKNG1E4d+4ojh/fhyJFijxHqZ8cu92O1atX44svvsCmTZuUt1jHBdJk\naDTZD2zx8fG5mnOlfPnySE5eC+CqciQRkjQf1auXz7U+VF4RMnsNeNE+qqnn+XPx4kUuXLiQ+/bt\ne96iPHWSkpJYvXp9WiwR1Gg6Uav1piA4UxDeVcxZBymKEZw8+ftM658/f57lyr1BrdZAs9mJffsO\nzrX1gMGDh9Fk8qAktaQkBfKNNxry/v37udK2yn8PPGsbf25+VMWv8ixZsWIFLZbiBK4S8CEwjMAm\nAqUJGOji4ssRI76h3W7PUNdut7NIkdeo0QwhkEDgPEUxkuPHT8g1+Y4fP86ZM2dyx44dmcqgopJC\nVor/qdn4VVReVvbv34/Y2FoAlkD2R/hEObMbovg2hg9/Hd26dcu07unTp3H69HnY7f+DbEnNh7i4\nzzB58lC8997Dc/mfP38ec+fOQ1JSEpo3b4agoKAMZYKDgxEcHPyYV6eiotr4Vf5DzJ8/H8WLV0JI\nSCRGjhyF5OTkx2qnWLFikKS1AG4AyJPm3P37ebKNStbr9SATATj2nQCDwfDQfrdv347Q0JIYMuQc\nhg6NRrFi5bBixYrHugYVlexQZ/wqLyUkMW7cRIwaNQnx8XGIiCiCbdu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vnrniBzAdcjKQ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o4bmtsp27t/p1brS6MxksAkGo2d6Orqq9jIuynytVZmxH9Qq7Wxdes2NJurUn4DOU7ZNDKZwJ8E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\nnvidcy7DeOJ3zrkM44nfOecyzP8BfwdZPZ1K+7MAAAAASUVORK5CYII=\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"23rUN1uTpoc4","colab_type":"text"},"source":["## Split data"]},{"cell_type":"code","metadata":{"id":"EHcoL7fH_CsS","colab_type":"code","colab":{}},"source":["import collections\n","from sklearn.model_selection import train_test_split"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"XJA0YhzxUWPP","colab_type":"code","colab":{}},"source":["TRAIN_SIZE = 0.7\n","VAL_SIZE = 0.15\n","TEST_SIZE = 0.15\n","SHUFFLE = True"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"_Mak_supAsIV","colab_type":"text"},"source":["Splitting the dataset for classification tasks requires more than just randomly splitting into train, validation and test sets. We want to ensure that each split has a similar class distribution so that we can learn to predict well across all the classes. We can do this by specifying the `stratify` argument in [`train_test_split`](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) which will be set to the class labels."]},{"cell_type":"code","metadata":{"id":"27h91LX0pp7F","colab_type":"code","colab":{}},"source":["def train_val_test_split(X, y, val_size, test_size, shuffle):\n","    \"\"\"Split data into train/val/test datasets.\n","    \"\"\"\n","    X_train, X_test, y_train, y_test = train_test_split(\n","        X, y, test_size=test_size, stratify=y, shuffle=shuffle) # notice the `stratify=y`\n","    X_train, X_val, y_train, y_val = train_test_split(\n","        X_train, y_train, test_size=val_size, stratify=y_train, shuffle=shuffle) # notice the `stratify=y_train`\n","    return X_train, X_val, X_test, y_train, y_val, y_test"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"D4fy2vUjr-Qe","colab_type":"code","outputId":"b10cd7cc-9107-44fc-a786-eeb0921be0ac","executionInfo":{"status":"ok","timestamp":1583943593621,"user_tz":420,"elapsed":2876,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":102}},"source":["# Create data splits\n","X_train, X_val, X_test, y_train, y_val, y_test = train_val_test_split(\n","    X=X, y=y, val_size=VAL_SIZE, test_size=TEST_SIZE, shuffle=SHUFFLE)\n","class_counts = dict(collections.Counter(y))\n","print (f\"X_train: {X_train.shape}, y_train: {y_train.shape}\")\n","print (f\"X_val: {X_val.shape}, y_val: {y_val.shape}\")\n","print (f\"X_test: {X_test.shape}, y_test: {y_test.shape}\")\n","print (f\"Sample point: {X_train[0]} → {y_train[0]}\")\n","print (f\"Classes: {class_counts}\")"],"execution_count":90,"outputs":[{"output_type":"stream","text":["X_train: (722, 2), y_train: (722,)\n","X_val: (128, 2), y_val: (128,)\n","X_test: (150, 2), y_test: (150,)\n","Sample point: [18.01865938 15.48133647] → benign\n","Classes: {'malignant': 611, 'benign': 389}\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"lLHG5_vpHQ3d","colab_type":"text"},"source":["## Label encoder"]},{"cell_type":"markdown","metadata":{"id":"YGWO8zDCHTFp","colab_type":"text"},"source":["You'll notice that our class labels are text. We need to encode them into integers so we can use them in our models. We're going to the scikit-learn's [LabelEncoder](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.LabelEncoder.html#sklearn.preprocessing.LabelEncoder) to do this. "]},{"cell_type":"code","metadata":{"id":"KPIsL1kAHkhu","colab_type":"code","colab":{}},"source":["from sklearn.preprocessing import LabelEncoder"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"hcfHtYFtHkmo","colab_type":"code","colab":{}},"source":["# Output vectorizer\n","y_tokenizer = LabelEncoder()"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"4hbPtvg4HoqE","colab_type":"code","outputId":"fc3c0398-fb08-48cb-c8bf-92579dc03eb3","executionInfo":{"status":"ok","timestamp":1583943593622,"user_tz":420,"elapsed":2773,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Fit on train data\n","y_tokenizer = y_tokenizer.fit(y_train)\n","classes = y_tokenizer.classes_\n","print (f\"classes: {classes}\")"],"execution_count":93,"outputs":[{"output_type":"stream","text":["classes: ['benign' 'malignant']\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"U7MTxcrcHotG","colab_type":"code","outputId":"073e0f85-a706-4871-8eee-baf0c6adf8d0","executionInfo":{"status":"ok","timestamp":1583943593623,"user_tz":420,"elapsed":2753,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Convert labels to tokens\n","print (f\"y_train[0]: {y_train[0]}\")\n","y_train = y_tokenizer.transform(y_train)\n","y_val = y_tokenizer.transform(y_val)\n","y_test = y_tokenizer.transform(y_test)\n","print (f\"y_train[0]: {y_train[0]}\")"],"execution_count":94,"outputs":[{"output_type":"stream","text":["y_train[0]: benign\n","y_train[0]: 0\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"sXHboWkUAIjI","colab_type":"code","outputId":"9550ee7a-2a3f-4bc9-a734-92a57ae3bd07","executionInfo":{"status":"ok","timestamp":1583943593624,"user_tz":420,"elapsed":2730,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Class weights\n","counts = collections.Counter(y_train)\n","class_weights = {_class: 1.0/count for _class, count in counts.items()}\n","print (f\"class counts: {counts},\\nclass weights: {class_weights}\")"],"execution_count":95,"outputs":[{"output_type":"stream","text":["class counts: Counter({1: 441, 0: 281}),\n","class weights: {0: 0.0035587188612099642, 1: 0.0022675736961451248}\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"nkAmzEwVHs6E","colab_type":"text"},"source":["**NOTE**: Class weights are useful for weighting the loss function during training. It tells the model to focus on samples from an under-represented class. The loss section below will show how to incorporate these weights."]},{"cell_type":"markdown","metadata":{"id":"IodMyhnAJUg_","colab_type":"text"},"source":["## Standardize data"]},{"cell_type":"markdown","metadata":{"id":"QRhNHi9YJfDm","colab_type":"text"},"source":["We need to standardize our data (zero mean and unit variance) in order to optimize quickly. We're only going to standardize the inputs X because our outputs y are class values."]},{"cell_type":"code","metadata":{"id":"rjIz1KKYJWI7","colab_type":"code","colab":{}},"source":["from sklearn.preprocessing import StandardScaler"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"hP6VTXSiJWM1","colab_type":"code","colab":{}},"source":["# Standardize the data (mean=0, std=1) using training data\n","X_scaler = StandardScaler().fit(X_train)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"kn2SDd28Jwna","colab_type":"code","colab":{}},"source":["# Apply scaler on training and test data (don't standardize outputs for classification)\n","X_train = X_scaler.transform(X_train)\n","X_val = X_scaler.transform(X_val)\n","X_test = X_scaler.transform(X_test)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"zBAu7GkJJwq8","colab_type":"code","outputId":"98f97bad-d2ad-48de-a08c-b6cbd4f56003","executionInfo":{"status":"ok","timestamp":1583943593794,"user_tz":420,"elapsed":2837,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":119}},"source":["# Check (means should be ~0 and std should be ~1)\n","print (f\"X_train[0]: mean: {np.mean(X_train[:, 0], axis=0):.1f}, std: {np.std(X_train[:, 0], axis=0):.1f}\")\n","print (f\"X_train[1]: mean: {np.mean(X_train[:, 1], axis=0):.1f}, std: {np.std(X_train[:, 1], axis=0):.1f}\")\n","print (f\"X_val[0]: mean: {np.mean(X_val[:, 0], axis=0):.1f}, std: {np.std(X_val[:, 0], axis=0):.1f}\")\n","print (f\"X_val[1]: mean: {np.mean(X_val[:, 1], axis=0):.1f}, std: {np.std(X_val[:, 1], axis=0):.1f}\")\n","print (f\"X_test[0]: mean: {np.mean(X_test[:, 0], axis=0):.1f}, std: {np.std(X_test[:, 0], axis=0):.1f}\")\n","print (f\"X_test[1]: mean: {np.mean(X_test[:, 1], axis=0):.1f}, std: {np.std(X_test[:, 1], axis=0):.1f}\")"],"execution_count":99,"outputs":[{"output_type":"stream","text":["X_train[0]: mean: 0.0, std: 1.0\n","X_train[1]: mean: -0.0, std: 1.0\n","X_val[0]: mean: 0.1, std: 1.0\n","X_val[1]: mean: 0.1, std: 1.0\n","X_test[0]: mean: -0.1, std: 1.0\n","X_test[1]: mean: -0.1, std: 1.0\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"CYH7kRTd9WoJ","colab_type":"text"},"source":["# NumPy\n","\n","Now that we have our data prepared, we'll first implement logistic regression using just NumPy. This will let us really understand the underlying operations. It's normal to find the math and code in this section slightly complex. You can still read each of the steps to build intuition for when we implement this using PyTorch."]},{"cell_type":"markdown","metadata":{"id":"Y-gUbD71-yiX","colab_type":"text"},"source":["Our goal is to learn a logistic model $\\hat{y}$ that models $y$ given $X$. \n","\n","$ \\hat{y} = \\frac{e^{XW_y}}{\\sum e^{XW}} $ \n","* $\\hat{y}$ = prediction | $\\in \\mathbb{R}^{NX1}$ ($N$ is the number of samples)\n","* $X$ = inputs | $\\in \\mathbb{R}^{NXD}$ ($D$ is the number of features)\n","* $W$ = weights | $\\in \\mathbb{R}^{DXC}$ ($C$ is the number of classes)"]},{"cell_type":"markdown","metadata":{"id":"6wcc5lbdH_Hi","colab_type":"text"},"source":["We are going to use multinomial logistic regression even though our task only involves two classes because you can generalize the softmax classifier to any number of classes."]},{"cell_type":"markdown","metadata":{"id":"YOTrUTpwWWba","colab_type":"text"},"source":["## Initialize weights"]},{"cell_type":"markdown","metadata":{"id":"o-Os5f8mad5_","colab_type":"text"},"source":["1. Randomly initialize the model's weights $W$."]},{"cell_type":"code","metadata":{"id":"jdPe3f01Wg6X","colab_type":"code","colab":{}},"source":["INPUT_DIM = X_train.shape[1] # X is 2-dimensional\n","NUM_CLASSES = len(classes) # y has two possibilities (begign or malignant)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"6x4heep29c_F","colab_type":"code","outputId":"b2d25607-7af7-48aa-8739-89e577d8c654","executionInfo":{"status":"ok","timestamp":1583943593795,"user_tz":420,"elapsed":2816,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Initialize random weights\n","W = 0.01 * np.random.randn(INPUT_DIM, NUM_CLASSES)\n","b = np.zeros((1, NUM_CLASSES))\n","print (f\"W: {W.shape}\")\n","print (f\"b: {b.shape}\")"],"execution_count":101,"outputs":[{"output_type":"stream","text":["W: (2, 2)\n","b: (1, 2)\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"FdnkMO9AWsNB","colab_type":"text"},"source":["## Model"]},{"cell_type":"markdown","metadata":{"id":"7Fh8YOJjae28","colab_type":"text"},"source":["2. Feed inputs $X$ into the model to receive the logits ($z=XW$). Apply the softmax operation on the logits to get the class probabilies $\\hat{y}$ in one-hot encoded form. For example, if there are three classes, the predicted class probabilities could look like [0.3, 0.3, 0.4]. \n","  * $ \\hat{y} = softmax(z) = softmax(XW) = \\frac{e^{XW_y}}{\\sum_j e^{XW}} $"]},{"cell_type":"code","metadata":{"id":"EXQkZOwW-otw","colab_type":"code","outputId":"f7deafe4-d2c6-43f1-b500-b80a312cdccf","executionInfo":{"status":"ok","timestamp":1583943593796,"user_tz":420,"elapsed":2789,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Forward pass [NX2] · [2X2] + [1,2] = [NX2]\n","logits = np.dot(X_train, W) + b\n","print (f\"logits: {logits.shape}\")\n","print (f\"sample: {logits[0]}\")"],"execution_count":102,"outputs":[{"output_type":"stream","text":["logits: (722, 2)\n","sample: [0.01817675 0.00635562]\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"Ak9FfYIJ-ozJ","colab_type":"code","outputId":"ab4cbcb9-658f-43b5-d24c-fccf224a8229","executionInfo":{"status":"ok","timestamp":1583943593796,"user_tz":420,"elapsed":2762,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Normalization via softmax to obtain class probabilities\n","exp_logits = np.exp(logits)\n","y_hat = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)\n","print (f\"y_hat: {y_hat.shape}\")\n","print (f\"sample: {y_hat[0]}\")"],"execution_count":103,"outputs":[{"output_type":"stream","text":["y_hat: (722, 2)\n","sample: [0.50295525 0.49704475]\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"qQ39Xr8QW22V","colab_type":"text"},"source":["## Loss"]},{"cell_type":"markdown","metadata":{"id":"VxxORg12amXv","colab_type":"text"},"source":[" 3. Compare the predictions $\\hat{y}$ (ex.  [0.3, 0.3, 0.4]]) with the actual target values $y$ (ex. class 2 would look like [0, 0, 1]) with the objective (cost) function to determine loss $J$. A common objective function for logistics regression is cross-entropy loss. \n","\n","  * $J(\\theta) = - \\sum_i ln(\\hat{y_i}) = - \\sum_i ln (\\frac{e^{X_iW_y}}{\\sum_j e^{X_iW}}) $"]},{"cell_type":"code","metadata":{"id":"_dfuMmW2Y01f","colab_type":"code","outputId":"7be7e1fe-4904-4201-f35e-e42d1b2e4cb9","executionInfo":{"status":"ok","timestamp":1583943593797,"user_tz":420,"elapsed":2743,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Loss\n","correct_class_logprobs = -np.log(y_hat[range(len(y_hat)), y_train])\n","loss = np.sum(correct_class_logprobs) / len(y_train)\n","print (f\"loss: {loss:.2f}\")"],"execution_count":104,"outputs":[{"output_type":"stream","text":["loss: 0.69\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"iIz5JF8rW5uM","colab_type":"text"},"source":["## Gradients"]},{"cell_type":"markdown","metadata":{"id":"g9nWUa-3b2lw","colab_type":"text"},"source":["4. Calculate the gradient of loss $J(\\theta)$ w.r.t to the model weights. Let's assume that our classes are mutually exclusive (a set of inputs could only belong to one class).\n"," * $\\frac{\\partial{J}}{\\partial{W_j}} = \\frac{\\partial{J}}{\\partial{\\hat{y}}}\\frac{\\partial{\\hat{y}}}{\\partial{W_j}} = - \\frac{1}{\\hat{y}}\\frac{\\partial{\\hat{y}}}{\\partial{W_j}} = - \\frac{1}{\\frac{e^{XW_y}}{\\sum_j e^{XW}}}\\frac{\\sum_j e^{XW}e^{XW_y}0 - e^{XW_y}e^{XW_j}X}{(\\sum_j e^{XW})^2} = \\frac{Xe^{XW_j}}{\\sum_j e^{XW}} = X\\hat{y}$\n","  * $\\frac{\\partial{J}}{\\partial{W_y}} = \\frac{\\partial{J}}{\\partial{\\hat{y}}}\\frac{\\partial{\\hat{y}}}{\\partial{W_y}} = - \\frac{1}{\\hat{y}}\\frac{\\partial{\\hat{y}}}{\\partial{W_y}} = - \\frac{1}{\\frac{e^{XW_y}}{\\sum_j e^{XW}}}\\frac{\\sum_j e^{XW}e^{XW_y}X - e^{W_yX}e^{XW_y}X}{(\\sum_j e^{XW})^2} = \\frac{1}{\\hat{y}}(X\\hat{y} - X\\hat{y}^2) = X(\\hat{y}-1)$"]},{"cell_type":"code","metadata":{"id":"9_-LGJWwZqhW","colab_type":"code","colab":{}},"source":["# Backpropagation\n","dscores = y_hat\n","dscores[range(len(y_hat)), y_train] -= 1\n","dscores /= len(y_train)\n","dW = np.dot(X_train.T, dscores)\n","db = np.sum(dscores, axis=0, keepdims=True)"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"Fuw-7BVrW-_M","colab_type":"text"},"source":["## Update weights"]},{"cell_type":"markdown","metadata":{"id":"QaOhLrqib7t9","colab_type":"text"},"source":["5. Update the weights  𝑊  using a small learning rate  𝛼. The updates willpenalize the probabiltiy for the incorrect classes (j) and encourage a higher probability for the correct class (y).\n","  * $W_j = W_j - \\alpha\\frac{\\partial{J}}{\\partial{W_j}}$"]},{"cell_type":"code","metadata":{"id":"8pDGJRmQXC39","colab_type":"code","colab":{}},"source":["LEARNING_RATE = 1e-1"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"qy6LjHNPZqe1","colab_type":"code","colab":{}},"source":["# Update weights\n","W += -LEARNING_RATE * dW\n","b += -LEARNING_RATE * db"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"TsxBN1l8XUVn","colab_type":"text"},"source":["## Training"]},{"cell_type":"code","metadata":{"id":"wa9N6rLtXVYB","colab_type":"code","colab":{}},"source":["NUM_EPOCHS = 50"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"AFjnVvCqb_Kk","colab_type":"text"},"source":["6. Repeat steps 2 - 5 to minimize the loss and train the model."]},{"cell_type":"code","metadata":{"id":"vCipe3EhZqbl","colab_type":"code","outputId":"bb62253e-adb3-497d-b246-a00ba51aa1e9","executionInfo":{"status":"ok","timestamp":1583943593799,"user_tz":420,"elapsed":2707,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":102}},"source":["# Initialize random weights\n","W = 0.01 * np.random.randn(INPUT_DIM, NUM_CLASSES)\n","b = np.zeros((1, NUM_CLASSES))\n","\n","# Training loop\n","for epoch_num in range(NUM_EPOCHS):\n","\n","    # Forward pass [NX2] · [2X2] = [NX2]\n","    logits = np.dot(X_train, W) + b\n","    \n","    # Normalization via softmax to obtain class probabilities\n","    exp_logits = np.exp(logits)\n","    y_hat = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)\n","\n","    # Loss\n","    correct_class_logprobs = -np.log(y_hat[range(len(y_hat)), y_train])\n","    loss = np.sum(correct_class_logprobs) / len(y_train)\n","\n","    # show progress\n","    if epoch_num%10 == 0:\n","        # Accuracy\n","        y_pred = np.argmax(logits, axis=1)\n","        accuracy =  np.mean(np.equal(y_train, y_pred))\n","        print (f\"Epoch: {epoch_num}, loss: {loss:.3f}, accuracy: {accuracy:.3f}\")\n","\n","    # Backpropagation\n","    dscores = y_hat\n","    dscores[range(len(y_hat)), y_train] -= 1\n","    dscores /= len(y_train)\n","    dW = np.dot(X_train.T, dscores)\n","    db = np.sum(dscores, axis=0, keepdims=True)\n","\n","    # Update weights\n","    W += -LEARNING_RATE * dW\n","    b += -LEARNING_RATE * db"],"execution_count":109,"outputs":[{"output_type":"stream","text":["Epoch: 0, loss: 0.684, accuracy: 0.889\n","Epoch: 10, loss: 0.447, accuracy: 0.978\n","Epoch: 20, loss: 0.348, accuracy: 0.978\n","Epoch: 30, loss: 0.295, accuracy: 0.981\n","Epoch: 40, loss: 0.260, accuracy: 0.981\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"2zHB-mHA1-Uh","colab_type":"text"},"source":["Since we're taking the argmax, we can just calculate logits since normalization won't change which index has the higher value. "]},{"cell_type":"code","metadata":{"id":"TpE3oDpIhhBH","colab_type":"code","colab":{}},"source":["class LogisticRegressionFromScratch():\n","    def predict(self, x):\n","        logits = np.dot(x, W) + b\n","        exp_logits = np.exp(logits)\n","        y_hat = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)\n","        return y_hat"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"-6T8rm1bw_Sw","colab_type":"code","colab":{}},"source":["# Evaluation\n","model = LogisticRegressionFromScratch()\n","logits_train = model.predict(X_train)\n","pred_train = np.argmax(logits_train, axis=1)\n","logits_test = model.predict(X_test)\n","pred_test = np.argmax(logits_test, axis=1)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"Smy3DxJazGFm","colab_type":"code","outputId":"cd87de02-c822-419e-cac6-253d7218875e","executionInfo":{"status":"ok","timestamp":1583943593800,"user_tz":420,"elapsed":2668,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Training and test accuracy\n","train_acc =  np.mean(np.equal(y_train, pred_train))\n","test_acc = np.mean(np.equal(y_test, pred_test))\n","print (f\"train acc: {train_acc:.2f}, test acc: {test_acc:.2f}\")"],"execution_count":112,"outputs":[{"output_type":"stream","text":["train acc: 0.98, test acc: 0.94\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"Cv-Dxp4AxeWh","colab_type":"code","colab":{}},"source":["def plot_multiclass_decision_boundary(model, X, y, savefig_fp=None):\n","    \"\"\"Plot the multiclass decision boundary for a model that accepts 2D inputs.\n","\n","    Arguments:\n","        model {function} -- trained model with function model.predict(x_in).\n","        X {numpy.ndarray} -- 2D inputs with shape (N, 2).\n","        y {numpy.ndarray} -- 1D outputs with shape (N,).\n","    \"\"\"\n","    # Axis boundaries\n","    x_min, x_max = X[:, 0].min() - 0.1, X[:, 0].max() + 0.1\n","    y_min, y_max = X[:, 1].min() - 0.1, X[:, 1].max() + 0.1\n","    xx, yy = np.meshgrid(np.linspace(x_min, x_max, 101),\n","                         np.linspace(y_min, y_max, 101))\n","\n","    # Create predictions\n","    x_in = np.c_[xx.ravel(), yy.ravel()]\n","    y_pred = model.predict(x_in)\n","    y_pred = np.argmax(y_pred, axis=1).reshape(xx.shape)\n","\n","    # Plot decision boundary\n","    plt.contourf(xx, yy, y_pred, cmap=plt.cm.Spectral, alpha=0.8)\n","    plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.RdYlBu)\n","    plt.xlim(xx.min(), xx.max())\n","    plt.ylim(yy.min(), yy.max())\n","\n","    # Plot\n","    if savefig_fp:\n","        plt.savefig(savefig_fp, format='png')"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"Z7RorJHHxfW7","colab_type":"code","outputId":"b3c5753e-9325-4762-f8b9-a8cf96d0269c","executionInfo":{"status":"ok","timestamp":1583943594897,"user_tz":420,"elapsed":3747,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":336}},"source":["# Visualize the decision boundary\n","plt.figure(figsize=(12,5))\n","plt.subplot(1, 2, 1)\n","plt.title(\"Train\")\n","plot_multiclass_decision_boundary(model=model, X=X_train, y=y_train)\n","plt.subplot(1, 2, 2)\n","plt.title(\"Test\")\n","plot_multiclass_decision_boundary(model=model, X=X_test, y=y_test)\n","plt.show()"],"execution_count":114,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAsEAAAE/CAYAAACnwR6AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7m4k/JULWKbdmvI4Rh6dqNlKU4JR3v9IsNvvghqOzNKSJ67L0cals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b7xyhFCoVDsFJdH\np+uBdroe2H06luJguPZcht8520D863+kBHANlAg+RRhFgzs/HKuKyE78ZBpfyEuwpVpIrsfX6L3v\n57sOzaVtuhQmhKCpN0RTbwiAfKLA1FuzpKNZNF3QciZCz0OdVRZnulunebCJ5YlERRRVaIJwTyNn\nPzXoeD6zZDLy8gSZhSyaJrBMSVNfiKGn+7Yd9QZb9M+8N09mMVflSLERayXlYTcIXVTn2NlbNtsL\ngODMFI2T4+hGZV6xXi4x9Dd/WSWCVwWwsspRKBQKxWlHieBTxOJo3DEx3jIl8zcWOPMJh1DuOjof\naLeLwzZEJ4UmiDikQtTC3+Tj/LPD23pt/5M9GCWT1FzaFrQrbgvrG1FsZPSVSTKxLNKSmCtjTUyn\nmHprloEne7d13sxijjs/uLetfGShCRpaA5il3RXnCSEIOkSymwec86k1XdB6xo7cB+dnkTXyf/1L\nCxU/rwrg7/y6SeIb3+aGigwoFArFCUaqYrgtUCL4FFFMFWvmpTpFeDfS2B5k4Fovk2/M2CvpUuIO\nuDn7qUF01/YjrDtBd2mc+5lBipkShXQRX4Onqpe9tKSdjiHsFIpUNFNl1yNNyeK9OH2PdW8rGjz1\n5uz2ivkEhLoaGHqmn9idJdLR7NZWQev8hTVd0PdYl+P7F2wJ0Hq2mcV78bXovebSCDT7aVlpkpFv\nbauZ1lAMV6e4fPPXEpivv6OWxhQKheKEshrweH7AwHz9ZTXfb4ISwaeIYGuApbFEdYGawDES6UTL\ncITIQJh8ooDm0vCFvAfSqc3b4HFMuUjOphl7dXJNsApdbNrDwiyZaP6tRXB2Kbf1oAS0X2yl/7Fu\nANrPNRO7uVC7m54uaD/fgmlYZBdyeBo8dF5uq6i+3kjf491E+sN2y2nDonmgiabekN1aGUj3D1Fo\nbSMwP4u2zn7N9HgY//yXtr6GY4KUkvxSglI2hzfUiD8SOuwhKRSKbWIUDcyyhSfoPtDOnqcRlfK2\nM5QIPkU0DzQx8+58lQjWdI3Oy9tvNKHp2pb5wwdBIVXk3kvjlRHb2pa7aLq21oFuFcuSzH0QZeHO\nEmbZItjip/fRLjSXtubzWwuhCTpWitPArqy+9HPnmHxjhuRMuvK1usATcNN9tQPdrW/7GoUQNHY0\n0NjRUOsFvPdPf4srf/j/0jgxhnTpCMti4rkvEn3yvjtENJ/iuBbDlfNFJl66TjlnF2ZKCf5IiP5P\nPIbu3lvBo0Kh2D/K+TKjr06RiWURAjS3Tv8T3Y5OQoq9s14Ad/yuSnnbDkoEnyI0l8alz59l/KfT\npOcySCAQ8TNwrWdfPR7Nskl8MolRNGloCxBsDSCEIJ8oMPt+lMxCFrffTeflNiID4S0jBaZhkVvO\n78h/WNMF3Q+2r0VQVxl9eYLkXHotTSSzkOPOC6M0tAdJzWUcjyV0+xiDH+utet+8DR7OfXoIy7JY\nHk8Qu7WEUTBoaA/S+1jXjqlasEYAACAASURBVATwdik3hnj3N34bb3wZdyZNrqMTy3M/ZWS9Vc5x\njAxMvf4OxXSmIryfX04w+9ZH9H3s4cMb2CmnXDAwiwaeBs+OCk4VpwMpJbf+7p5tdbnSM8kyDcZf\nm8LldRHqrPFgr9gVG2s+VArE9lAi+JThCXo4/5lhLNNCSvYtl1dKSSlXJh8vMPrKJCCxTGlHkVsD\ndF/t4O6PRtcaUJTzBuOvT5FLFOh9uLPmcedvLDD73jxoYstI7RoCeh7tov18S8Wv84lChQBexTIl\n6U2cHnoe7qT1TDMuT21BKxCkZtPkkwXALsxLTKc4+zODO578V1uSbiU0ipFmipHmit+tCuD9Xhor\nZfNE37tFes7uvhHq6aDz4Uu4fN4t9tycci5PYTnp2Mo1PR3FMkw0V/0fLBS1MYoGY69OkZrP2A+V\nAnquduxr23LF8SM1l7G7YW747lqmZPb9qBLBdUL5Ae8NJYJPKfsZuVkajzP15hxmyaiy/rIMi8xC\nltFXJqs6sFmmJHpjgY6LrY7d0+JTSWbfm7ejvzvoQIeEUrbM3R+P4fK6aD/fQkNbkOxSzm5i4bRL\nje5wmkvD7XVtKoAB5j6KEZ9Mrl2/XDnLyIvjPPRfXd7Ww4dZNpl6c5alsQTSkvibvPQ93rOjm4cl\nTb75awnOXt8/AWwUS4y+8Bpm8X5xZXJqnuxCnHM/9wk01+6nGaNYQmga0qHdNIBZNpQIPmDu/GiM\nfDyPtFgrAp15dx6X17VWsKnYXwqpIvM3F8gt5/GHfXRcaiUQ2d+umTulkCrWLBIurAQHFPVB+QHv\nHrWGpagrybk0E69PYxSqBfAq0pSUc2XHbUITNf125z7YXgtlJ6I3F0jNZlgeS3DnhVHmPozh8rnY\nshXcBizDYvaDKPFJ585wpWyJW98fYfa9aM3rT0w577seKSV3XhhdE8AA+USRkR+PkVncRtHeARK/\nN4lV3pCMLSVmqUxiYnZPx/Y2NtS0+NHcLlw+1ar1IMku5SgkCtUPt6Zk9oPo4QzqlJFZyHLjb++w\nOLJMbinP0licW98bsVu2HyG8jZ6q9LO1baHaK0TSkpiGpay9FAeCEsGKujL7XnTXQnWVWnmzpdzW\nNm41WTek1eU4f9iHtot0kGK6xNirk8y+X3nTtyzJre/f21SkSim35SecWciRT1ZHUixT2ukgR4hs\nbNkxUitNk2xsaU/H1lw6bZfPIPTKz4TQNTofuqgqzQ+YYrpk9wB3oJR1frBV1Jfx16ftVbTVqUHa\n88L461Nb2zMeIOGuRlxevSrOYNdndFS93jIsJq7P8Pa3PuSdb33IB391i/hk4oBGe/yp90NDOV8g\ntxjHKBTretyjhhLBirpSSG3vC+MJuh2jBJoualqGBZrquNwnbHu1888O4fK51ordtotlSuY+imEU\n70dAkzMpjJJZ259thYZNLNFW2dhaeuO27bBaKHFBbyT93bFt7bMb3AGfc0BdCNyBvf/NWi8O0/XY\nZTwNAYSm4Q010Puxh2ka7NnzsRU7wxfy1nQY8QS379QhLUluOU8+WVARvx1QLhh2oZkDlinXahCO\nAkITXPzcGYItAYQm0Fwauken/4kewt2NVa8feXmCxZFlu0ZjJYVt9NUpEjNHK8J9lFjNB35+oFw3\nP2DLMJl89W3u/peXmPj7N7nzNy8y9ZN3sczdNYM66qicYEVd8TZ4Nhdpws5HPvPJASbfmCWfKGBZ\nFpqmIQSc+8xQzSW07oc6yCxkKyLNQhO7in4I7IBWIOLnoV+6RGI2zehL4ztyELNTN3Jr7aALqSKW\nWbtYT+iCpp7QtnL3Vh8SnK7NHdhabMzllg+sUKL53ADJqTnkhmsXmiAyXLuz33YRQhAZ7CUyuL1u\nf4r9I9Dsxx/xVz2kabqg+2p1dM+J+FSS8den7f2lxOV3c+YT/UfCdvGos+nCh9y6ePag8QQ9XPr8\nWUq5MmbJxBvyojnM7/lkgXSNJkcz78zT1KN8wTeyX37AM298QGZuAWlZayt86Zkocy6dnscfrMs5\njhJH6xujqAtGySQdzRxKVKD7ageaQ1RVaOD2u2gebOLyF84RbAlw8WfPcO7Tg/Q+3MXAtR6uPn+5\n5o2wnC/jCbg586kBvI0eECsiqz+EN1Q7LzTU3eAoqqWE8MrEKjRBpDdE69nmqoiw07XcPwjo6wrk\nfCFvzZuQ0AW9D3cy/PH+2sdbR7i70TFVQ9MFXVfaN913Lhfn2nPpA6sU9kfCdD1yGaFraC4XmktH\n6Do9T17F27h11FtxvDj3mSFC3Y0r0T2B7tboebSLlqGti+Jyy3nGXpnELJlYhoVlSkqZErdfGK1Y\nVVE44/K6CLY4P0S7/W57bjyCeAJu/E0+RwEMkI8XaqY2bXd18TSx6vtebwFsFEukZ6JV6W3StEiO\nz2IZJ+87qiLBJwgpJbPvRZm/uWALP0vibfRy9tODeIMHMzk29Yboe7yb6bfnkNIeU7DZz/AnBvBs\niGBu2QgCO0Iw9uok+UQRBHj8bgaf7iMQ8dk3YV0jMZ1i9O8nKnORBTR2BOl7tJuRl8Yp5w27SciK\neO59uLNqPH1P9ICAxXtxhBBIKWk914JpmCyPJqqiFJpLo6HtvmgP94RweXRKplWVEtF2tpnWM81r\ngtyyLAqJIlJKAhF/lVDXdI0Lzw1z98fjGAUDhL2E3HmlnebBrY3mnx80D7RdZmS4j1BfF9nYEkJA\nsL1VuTacUFwenXM/M4hRNDBKJp6gp6a42cj8jQXnmgFLsjQWp+OislnbisGn+7j1vREs08IypN0l\nUxOc+eSAo5A0y+baXLmKZVos3F1icWQZy5Q0DzTRcbltS9eb/WKzVBqXg1OQwnaEuOgOE//uGDBY\nl2MaheLKCqTDRiEwiiU8e3D7OYqcrKs55SzeW2b+Rsy2Llq50eSTBW7/YJQrXzpHOppFmpLGjmBV\n57R60nauhZbhCMV0Cd2jV4nN7WKUTG59/15FIVkxU+LuD0e5/MXzdn4itvAeeKqX6bfmMIomEkmg\n2U9uKc/N795FSgi2+HF5Xbj9LtrOteALe0lMp7BMi1BnAy6vC00TNA/a4y6kSwRbA7Sda8YTcJNf\nLqylO2j6SurGpwcRQlDOl4neXiQ9l8Ef9qJ5dNsCaN29fnFkmeXxBH1PdDPz7jyljF1EJDS7EHDo\n4/2Euyrz5PxhHw/+/AVyy3nMkkmgJXBoN6ntoLtdhHq2tySuOP64vK4dzyO1onqWKVXEb5v4Gr08\n+AsXWRpLkIvn8Ye8tAxHqv4W6ViWyesz5JN2lDXc08jAtV5cXp27P7JdZlbvE/M3FlgaT3DlC+cq\nVrcOimBrAHfAZRderps3NV3sqJupYm+4A/6aOfpCsGff96OIEsEnBKNoMHl9tvoJTtqpBO/+xxtr\n0UZpSrof6thyWX2nFJIFjJKJv8mH7tbxN/m23McsmxTTJdwBd5U38NJYvCrPFGwXhvmbCwxeu58j\n2jIYoXmgCbNsMfdBlNjtpYrIbXY5T7jbvgkkZ9Pc+rt7a8Vc0pT0PNSBy+ti8o2ZtUhVKVsiOZXk\n/GeHufRzZ0lHs2SXcngCbpr6wugujWK6yI3vjmAZ1v3zafbkvd4H2TIllmky9spUxbVIC4yiyb0X\nx7nypfN4GysnGSHEjnIlj3N7ZMXJJ9DsJxfPV62UaC6NQLPKCd4uuluvav6znlw8z90fjq7NZVJK\nEtMp8okR+h7tIruUr2gSJC1JOV9m4e4SnXW+L2wHIQQXnh3m7ovjFFN2NNKyJG3nW2i/UPs6TyOr\nxXDI+tvI6W4XzWf7WR6ZQq4rhBO6TsuFITT96AZhdosSwSeEkZfGaxaIrU526ye9ufejBJr9VdHH\n3VDMlBh5cZxiuggraRhdV22RLaXEKJroLq0ix1VKyfTbc8TuLNnLL6Yk1N3I8DN9axZp+XjeeelU\nQt6h+M4yJSMvjpGJVVuUSVOSnE2TXcpx76XxquPOvDcPQlR2j1uxHpr46QxXvnSeUGdDVaOKqbfm\nqi3PLFuo7wTLksTuLNH3WPeO9lvPfhVK7AVpWRRTGYSu2+4OytLsVNN5uY3l8YSdmrSKsEXwdtJ8\nTiqWJcku5kBKgq2BPRe4OXqqS7szZ+zucuX7v7rZlMQnk4cignPxPOlolo6LrfjCXixDEoj49nXF\n8jhyEN3hOq5eRNNdLN0ZQ1oSoWu0Xhym9eJwXc9zVFCfsBNAIV0ku7Q926xVVruz7VUES0ty++/u\nUcqX7ejOysQ7936UUrZMYjJp24YBkf4wA9d60N06cx/GWLizhDTlmvBMzaa59/IE55+1v2z+sA+h\ni6q2xggco8zTb89t6tErNEHszpJjkFRagHAWjflkAbNsork08gm72NDf5EMIQXIuvdnbs30kFJK7\nXw4+igI4OT3P3JsfrlQZSzSXTnigm5bzg3iCKup3GvGFvJx/dojxn0zbS99Igm1Bhp7q27cW7ked\n5Gya0Vcm16J6AjvvN9IX3vUxazn0WIaFVTbtkzhMEQedCiEtyeirk3ajD2mnhyHhzKcGlQDewEYB\n/MFXX6JeucDrEULQ/sA52i6fwSwb6G5nO9OTgvqUnQBKmRKaJjB32KSinN97pWdqPuPojWuZkoU7\nlY0S4pNJSrkyF54bJupQICMtSTqWpZgp4W3w0DIcYfb9aNV1aZqgY0OemJSSpXvLUNuhDGlJ5Pq0\nhaoXOP9aYOfXTfxkGrNsn0B3aww9sz2nh+3iDuzt67jf7ZFXkVKSmppj8fYYRqFEoDVC+5WzeEP3\no+T55SQzP32vIp3FLFks351g+d4kXY9cpvlMfd8/xfGgoS3IA1++gFE0EEIcSg7qUaGYKTmuTI29\nMonvC+fwh7dOKXPC0+Bx9BPWXBrhnkayy/mq4ILm0mg7V5l6UC4YJKZTSEsS7m7E21DfAuuFu0sk\np1P3VytXpot7L41z9fnLR7oG4jBY3x55PwTweoSm4fIeTbeRenI6H72PCLnlPNPvzDH11uyeWuH6\nwr6aXdqEJpz/yprtnrBXipnStvOSpCXJLeXILOYwHZbjwBa4q5O3y+viwufO4At5EbpA0wVuv4sz\nnxqsvjmspC7URNg3382MNms1zJAS7r1432HCMizKeYORF8fwh7coFFg5pNCEffxNHqiXxhKko5nN\nj3cEiL5/m5k3PqQQT2HkC6Sm5xh94TUKifum9ou3Rh3zuQGwJPPv3KSc29nqheJk4fK6TrUABuzV\nMIf507Iksdu777bYdaWthlWloP1iG72PdK65SiDsua95sImmvvt+vIv3lnn/2zeZenOWqbdm+fA/\n32b67bldj8mJ2O0l53lbbK+9vEKxV1QkuM5YpoWUbLm0N/XmLAt3708AC3eWaB5qYuBa747zJj0B\nN5GBMPHJZMXTvaYL+h7vJnprkWK6VBEB1XWtqupWSklqLkN8IoHQBC3DEVs4bkIgYqcFyK3apK0i\nBPl4AZdHxyhWd6CxTLnm+mAf388DX7lgi23TwhvyOr4/QhP4mnwUEs7eyKHOBjqvtDFxfabm0EJd\nDWSiWVugb0ync0yhkHgaPOSWnc/pDXlobA9SSJVoaA3QdqGF6M1FYrcWHV8vTcnkm7Nc+eL5deeV\nawV5br+bSF+oRlvpgymGK+cLLN+dqPSRlHaXofn3bjH4qScBKKa2FvOp6Xlazg/t11AViiNPIV10\ntqOS2DUWG7BMi9Sc3VRiM5efUFcjfY93M/XW3Frqg8urc/ZnBtFdGh0X22jqXblnWJJwT2NFE59i\nusjE9Rk7XW3dZBi7s0hjR3DNY32vmGXnLmTSYi2Nbi+spZicgFoES5qAREp5YNaXpwElgutEuWAw\n8dNpkjNppJT4wz76n+xxbAGcjmUrBDDY4m95PEmkL7yrCWbwqT7cPhcLd5eRlkT36PQ81EHbuRYi\nA01MvzPH8njCLkDraqDvsW4867yDpSUZeWmcdDS7VjSxNBqn9Wwz/U/Ubk8bbA3gD3vJxQvb6txm\nGRaT12fQ3FpVR7TVjmpOlmrbWYbrf7ybkR+PVXaU0yHcHSK7kGPkxQnHgpBVdJfGlS+d5/2/urXl\nuYA1K7pAi91Ba71wFrqg/7Huqr9l/+PdBFv8TPxk2jECkl95H4UmMA2LOy+M2l31VqzZJt+Y4fyz\nwzS02jm16/PELrhCJOroGelEbjFe00cytxBf+7cvEqKYztRMMZHS2vRvoVCcBhragiRnUlXfJ6EL\ngm2VefPJ2TT3/n7C/k6t+Ib3XO2oWcjWdq6FlqEI2eU8ultbq2NYxdvgqWk/tjgad45QG5Lo7aW6\nieBQVyNLo/Gq3wtBVRHyTiikbBG/urIW7m5k4MmeinvecWK15uP5AQPz9ZfrcsxyrsDCzXtk5hbQ\nVlwhIsN9J+KBYScoEVwHpCW59f0Rexl/Zd7IJwrc/eEol37uXFUR19K9ZUcBZBkWiyPLu5pgNE3Q\n91g3vY90YRoWultb+zC7PDqD13orLMU2Ep9MVghgsIX54sgyzYNNNSPCQgjOPTvM5PVpO6og7ch0\nuDfE0ojzdQJYZWulhfKKbRvQMhSh/4nduyOEOhs4/9lhpt+ZJx/P4/K5aDvXzMx70eriOgcKqSLJ\n2fSaW8V28DR6GH6mn4nr08Qn7XQAl1enz0EAr+Jr9K6kZVSfY33KxMy7cxXtaVf/NiM/HuOh5y8T\nK6b3vVJ4I7q79pSxvjlG68VhUtPRCpud9QhNo6FL+X8qTje6V3d8oBSaoP1869rP5XzZMXd4dsXl\nJ1SjwFlzaY6BmK0wimbN+op6dvbrvtpBYiq5VmsB9j0htM328k6U82Vufm+kwrUnOZPmxndHePDn\nL9RYSTu6rC967vjdb3OjDnN8OVfg3t+9glk21lYQ59+9STa2RN9Tj+z5+McJJYLrQGImZReZbSwO\nsySzH0Q584mByt9vIrBq5cpuF6GJXRUTLN5zts2xI9SJTdMiCqki6VgOhEAIexmrsT2I2+di/sMY\nCOEc9ZPgDrq58OwwutdVl+rwhrYgFz93Zu3n2Q+iNaORG8ktF5h6a27bAhggPpag75Euhj8+gGVY\nmIaFy6tv+jQdaPHj8uqUNrwnqykoq/su3os7RtctSzI5GcPT7ubaZ1P89sJbfPBNyX4XSgAE21sQ\nmgZUiluhaTQN3X/I8oUbGfjk48xcf59ytjL3V+g6od4O/JH6RJMUiuOI7e3unJ7Vdra5wjd9aSzu\nmO1kmZLorcWaIni3hLsaWBqNV83bQhM09dTvXN4GD5e/eJ7Z96OkZtNoHo32862beiBvRezOkvO9\nrGyyOBqn40Krw15Hk1Xf9+/8ukniG9+uW5Bj4cZIhQAGuzVyejZGPp46VXOzEsF1IB8v1BR5OQfr\nskh/2O5W5rBPIV3CLJt1eVrNJwtMvzVHaj6D0AUtQxF6H+50LEbZLJVhM8/bcsHgzgujFdciTcno\n308idGgZasbtdzF/Y8FRXJYy5U2XqKSU5JbzFNNFzLKF7tYJdTVU5cKZhsXSaJzEdBLdrdN2voVQ\nRwOFVHFbaRpr17rDhxCjaBKfTNIyFEHb4IVcCyEE5z49xO0f3MMy5Vr6g7/JR9+jXWuvqyXGpZSY\nZYNv/mrmwO3QhKbR//HHmHj5TUCupWn4mkK0XzlX8dpgWzPnvvApiuksibFpMvOL9rLbmX7C/V3O\nJ1AoTgnxqVTNeorEVKrCM7yUM2rOY6Vcue5jC/eE8IW95BOF+/OQZq9ytddZRHobPAw93Ve342Vi\nWefggSnJxLLHSgSD7QgB/rqu8qXnFhxrSKSUZGNLSgQrdoYn6EZzaY4CytNQnd/a1Bsi0OxzbOpQ\nzpWZfmeegSdr5+Fuh2KmxM3vjdhpB9gid3FkmUwsy+UvnKvy/WsZipBdzFVFqTWXRvNAbRP7pXvL\nNd0hpGnnFXtDnpqT/cYucesppIvc/dEYpWz5/qQm7P8GnuhZs/MxSiY3vzdCKXO/yCQ+kcTb6KF5\nqMnZa7iOxO4s0TIUAez32TItNJe2aTTY3+Tj6i9dIjmbppwrE2j2E2ytbCbR0BYgHc1W7Sstyf/1\nm3nOvvHeofgBB1ojnP/yp0nPRDEKRfwtTQRaI84Fi0LgCzXQ+dBFeOjAh6pQHFmsTewarQ3OKo3t\nQRZHqlfrhAaNe8idrYXQBBeeO8P8RzGWRu0Vqaa+MN0Pth95/15vo4d0LFu1Aig0e5vCTmszHMx5\nhNDQXEf771tvlEVaHYgMNDmaSWu6cGxNLDRB14MdjvtISzoWCuyUuY9iVROmtCTFTInkbHWDh+ah\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C+vUACFE38xC6F8HRaW/J8/1x4PDamXh9tOb8VYvCxOujjz35bvTyIHO/rrXKVFTB0HP9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nHlFqnFNYS63cvVYmtC6pJcZIuVDy63Hq4QCsEpQ3Db3E5s7pPfdnpS2Lo937RLYMRBZ4+19aVD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\nKIqiKMq+8/8Dsjxjjv/arLAAAAAASUVORK5CYII=\n","text/plain":["<Figure size 864x360 with 2 Axes>"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"QW5piG-XCz1N","colab_type":"text"},"source":["Credit for the plotting functions and the intuition behind all this is due to [CS231n](http://cs231n.github.io/neural-networks-case-study/), one of the best courses for machine learning. Now let's implement logistic regression with PyTorch."]},{"cell_type":"markdown","metadata":{"id":"7Cy3efR7s7HD","colab_type":"text"},"source":["# PyTorch"]},{"cell_type":"markdown","metadata":{"id":"hsnnH37eYxql","colab_type":"text"},"source":["Now that we've implemented logistic regression with Numpy, let's do the same with PyTorch. "]},{"cell_type":"code","metadata":{"id":"mWEfPoXzYxym","colab_type":"code","colab":{}},"source":["import torch"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"jVS_h2-cZW6U","colab_type":"code","outputId":"ff69689d-8346-4952-a244-58f2f05970f5","executionInfo":{"status":"ok","timestamp":1583943594899,"user_tz":420,"elapsed":3693,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Set seed for reproducibility\n","torch.manual_seed(SEED)"],"execution_count":116,"outputs":[{"output_type":"execute_result","data":{"text/plain":["<torch._C.Generator at 0x7f2e5a59e2f0>"]},"metadata":{"tags":[]},"execution_count":116}]},{"cell_type":"markdown","metadata":{"id":"-h-dlCTaYowa","colab_type":"text"},"source":["## Model"]},{"cell_type":"markdown","metadata":{"id":"CuGUAtHkyFBv","colab_type":"text"},"source":["We will be using Linear layers to recreate the same model."]},{"cell_type":"code","metadata":{"id":"7-vm9AZm1_f9","colab_type":"code","colab":{}},"source":["from torch import nn\n","import torch.nn.functional as F\n","from torchsummary import summary"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"p63Ws2STYolf","colab_type":"code","colab":{}},"source":["class LogisticRegression(nn.Module):\n","    def __init__(self, input_dim, num_classes):\n","        super(LogisticRegression, self).__init__()\n","        self.fc1 = nn.Linear(input_dim, num_classes)\n","        \n","    def forward(self, x_in, apply_softmax=False):\n","        y_pred = self.fc1(x_in)\n","        if apply_softmax:\n","            y_pred = F.softmax(y_pred, dim=1) \n","        return y_pred"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"6kJgaEqIcyHR","colab_type":"code","outputId":"df21ba13-53d3-4e95-d7a2-38e25fe7565d","executionInfo":{"status":"ok","timestamp":1583943594900,"user_tz":420,"elapsed":3654,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":306}},"source":["# Initialize model\n","model = LogisticRegression(input_dim=INPUT_DIM, num_classes=NUM_CLASSES)\n","print (model.named_parameters)\n","summary(model, input_size=(INPUT_DIM,))"],"execution_count":119,"outputs":[{"output_type":"stream","text":["<bound method Module.named_parameters of LogisticRegression(\n","  (fc1): Linear(in_features=2, out_features=2, bias=True)\n",")>\n","----------------------------------------------------------------\n","        Layer (type)               Output Shape         Param #\n","================================================================\n","            Linear-1                    [-1, 2]               6\n","================================================================\n","Total params: 6\n","Trainable params: 6\n","Non-trainable params: 0\n","----------------------------------------------------------------\n","Input size (MB): 0.00\n","Forward/backward pass size (MB): 0.00\n","Params size (MB): 0.00\n","Estimated Total Size (MB): 0.00\n","----------------------------------------------------------------\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"alKyigoqa9w9","colab_type":"text"},"source":["## Loss"]},{"cell_type":"markdown","metadata":{"id":"NLkVlnQJaQ4q","colab_type":"text"},"source":["Our loss will be the categorical crossentropy. "]},{"cell_type":"code","metadata":{"id":"wux5LwEGbFI7","colab_type":"code","outputId":"517636d7-e50c-45fd-d5e8-dcda2ca7e105","executionInfo":{"status":"ok","timestamp":1583943594901,"user_tz":420,"elapsed":3631,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["loss_fn = nn.CrossEntropyLoss()\n","y_pred = torch.randn(3, NUM_CLASSES, requires_grad=False)\n","y_true = torch.empty(3, dtype=torch.long).random_(NUM_CLASSES)\n","print (y_true)\n","loss = loss_fn(y_pred, y_true)\n","print(f'Loss: {loss.numpy()}')"],"execution_count":120,"outputs":[{"output_type":"stream","text":["tensor([0, 0, 1])\n","Loss: 1.6113080978393555\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"fl5kYzXVcahy","colab_type":"text"},"source":["In our case, we will also incorporate the class weights into our loss function to counter any class imbalances."]},{"cell_type":"code","metadata":{"id":"4gsEd7Mccarr","colab_type":"code","colab":{}},"source":["# Loss\n","weights = torch.Tensor([class_weights[key] for key in sorted(class_weights.keys())])\n","loss_fn = nn.CrossEntropyLoss(weight=weights)"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"f9oyIzgccYLy","colab_type":"text"},"source":["## Metrics"]},{"cell_type":"code","metadata":{"id":"rwzXNiPZcaCU","colab_type":"code","colab":{}},"source":["# Accuracy\n","def accuracy_fn(y_pred, y_true):\n","    n_correct = torch.eq(y_pred, y_true).sum().item()\n","    accuracy = (n_correct / len(y_pred)) * 100\n","    return accuracy"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"94eG68-OzrWt","colab_type":"code","outputId":"4508718e-3d71-4e16-d63b-9f6a7a62897d","executionInfo":{"status":"ok","timestamp":1583943594902,"user_tz":420,"elapsed":3595,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["y_pred = torch.Tensor([0, 0, 1])\n","y_true = torch.Tensor([1, 1, 1])\n","print(f'Accuracy: {accuracy_fn(y_pred, y_true):.1f}')"],"execution_count":123,"outputs":[{"output_type":"stream","text":["Accuracy: 33.3\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"m2zZs70qaOWn","colab_type":"text"},"source":["## Optimizer"]},{"cell_type":"code","metadata":{"id":"DWeLpGaIa64l","colab_type":"code","colab":{}},"source":["from torch.optim import Adam"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"oqzC6hRla7FN","colab_type":"code","colab":{}},"source":["# Optimizer\n","optimizer = Adam(model.parameters(), lr=LEARNING_RATE) "],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"BTjMYiOQcqNb","colab_type":"text"},"source":["## Training"]},{"cell_type":"code","metadata":{"id":"1X9BaZWwdD0P","colab_type":"code","colab":{}},"source":["# Convert data to tensors\n","X_train = torch.Tensor(X_train)\n","y_train = torch.LongTensor(y_train)\n","X_val = torch.Tensor(X_val)\n","y_val = torch.LongTensor(y_val)\n","X_test = torch.Tensor(X_test)\n","y_test = torch.LongTensor(y_test)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"hA7Oz97NAe8A","colab_type":"code","outputId":"e5d0b69f-225a-4a54-b353-7ceef37ce1a4","executionInfo":{"status":"ok","timestamp":1583943594903,"user_tz":420,"elapsed":3557,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":102}},"source":["# Training\n","for epoch in range(NUM_EPOCHS):\n","    # Forward pass\n","    y_pred = model(X_train)\n","\n","    # Loss\n","    loss = loss_fn(y_pred, y_train)\n","\n","    # Zero all gradients\n","    optimizer.zero_grad()\n","\n","    # Backward pass\n","    loss.backward()\n","\n","    # Update weights\n","    optimizer.step()\n","\n","    if epoch%10==0: \n","        predictions = y_pred.max(dim=1)[1] # class\n","        accuracy = accuracy_fn(y_pred=predictions, y_true=y_train)\n","        print (f\"Epoch: {epoch} | loss: {loss:.2f}, accuracy: {accuracy:.1f}\")"],"execution_count":127,"outputs":[{"output_type":"stream","text":["Epoch: 0 | loss: 0.95, accuracy: 60.8\n","Epoch: 10 | loss: 0.27, accuracy: 86.7\n","Epoch: 20 | loss: 0.15, accuracy: 96.1\n","Epoch: 30 | loss: 0.11, accuracy: 98.2\n","Epoch: 40 | loss: 0.09, accuracy: 98.9\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"Ufw6JQVLcuSS","colab_type":"text"},"source":["**NOTE**: We used the `class_weights` from earlier which will be used with our loss function to account for any class imbalances (our dataset doesn't suffer from this issue)."]},{"cell_type":"markdown","metadata":{"id":"dM7iYW8ANYjy","colab_type":"text"},"source":["## Evaluation"]},{"cell_type":"code","metadata":{"id":"uFXbczqu8Rno","colab_type":"code","colab":{}},"source":["import itertools\n","import matplotlib.pyplot as plt\n","from sklearn.metrics import accuracy_score\n","from sklearn.metrics import classification_report\n","from sklearn.metrics import confusion_matrix"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"hkFAI-z65m9m","colab_type":"code","colab":{}},"source":["def plot_multiclass_decision_boundary(model, X, y):\n","    x_min, x_max = X[:, 0].min() - 0.1, X[:, 0].max() + 0.1\n","    y_min, y_max = X[:, 1].min() - 0.1, X[:, 1].max() + 0.1\n","    xx, yy = np.meshgrid(np.linspace(x_min, x_max, 101), np.linspace(y_min, y_max, 101))\n","    cmap = plt.cm.Spectral\n","    \n","    X_test = torch.from_numpy(np.c_[xx.ravel(), yy.ravel()]).float()\n","    y_pred = model(X_test, apply_softmax=True)\n","    _, y_pred = y_pred.max(dim=1)\n","    y_pred = y_pred.reshape(xx.shape)\n","    plt.contourf(xx, yy, y_pred, cmap=plt.cm.Spectral, alpha=0.8)\n","    plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.RdYlBu)\n","    plt.xlim(xx.min(), xx.max())\n","    plt.ylim(yy.min(), yy.max())"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"-RnQrNaKQhWJ","colab_type":"code","colab":{}},"source":["def plot_confusion_matrix(y_true, y_pred, classes, cmap=plt.cm.Blues):\n","    \"\"\"Plot a confusion matrix using ground truth and predictions.\"\"\"\n","    # Confusion matrix\n","    cm = confusion_matrix(y_true, y_pred)\n","    cm_norm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]\n","\n","    #  Figure\n","    fig = plt.figure()\n","    ax = fig.add_subplot(111)\n","    cax = ax.matshow(cm, cmap=plt.cm.Blues)\n","    fig.colorbar(cax)\n","\n","    # Axis\n","    plt.title(\"Confusion matrix\")\n","    plt.ylabel(\"True label\")\n","    plt.xlabel(\"Predicted label\")\n","    ax.set_xticklabels([''] + classes)\n","    ax.set_yticklabels([''] + classes)\n","    ax.xaxis.set_label_position('bottom') \n","    ax.xaxis.tick_bottom()\n","\n","    # Values\n","    thresh = cm.max() / 2.\n","    for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):\n","        plt.text(j, i, f\"{cm[i, j]:d} ({cm_norm[i, j]*100:.1f}%)\",\n","                 horizontalalignment=\"center\",\n","                 color=\"white\" if cm[i, j] > thresh else \"black\")\n","\n","    # Display\n","    plt.show()"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"-jZtTd7F6_ps","colab_type":"code","outputId":"2cdf145a-e258-4ea5-987b-d2378f5668b4","executionInfo":{"status":"ok","timestamp":1583943594905,"user_tz":420,"elapsed":3530,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Predictions\n","pred_train = model(X_train, apply_softmax=True)\n","pred_test = model(X_test, apply_softmax=True)\n","print (f\"sample probability: {pred_test[0]}\")\n","pred_train = pred_train.max(dim=1)[1]\n","pred_test = pred_test.max(dim=1)[1]\n","print (f\"sample class: {pred_test[0]}\")"],"execution_count":131,"outputs":[{"output_type":"stream","text":["sample probability: tensor([0.0964, 0.9036], grad_fn=<SelectBackward>)\n","sample class: 1\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"sEjansj78Rqe","colab_type":"code","outputId":"31b42f93-cfbf-42c2-b506-3712f4233c4b","executionInfo":{"status":"ok","timestamp":1583943594906,"user_tz":420,"elapsed":3500,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Accuracy\n","train_acc = accuracy_score(y_train, pred_train)\n","test_acc = accuracy_score(y_test, pred_test)\n","print (f\"train acc: {train_acc:.2f}, test acc: {test_acc:.2f}\")"],"execution_count":132,"outputs":[{"output_type":"stream","text":["train acc: 0.98, test acc: 0.95\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"t9uDMe_Dh4cs","colab_type":"code","outputId":"4672e197-d4a0-4e24-ccc2-d78a7804bedb","executionInfo":{"status":"ok","timestamp":1583943595183,"user_tz":420,"elapsed":3750,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":336}},"source":["# Visualize the decision boundary\n","plt.figure(figsize=(12,5))\n","plt.subplot(1, 2, 1)\n","plt.title(\"Train\")\n","plot_multiclass_decision_boundary(model=model, X=X_train, y=y_train)\n","plt.subplot(1, 2, 2)\n","plt.title(\"Test\")\n","plot_multiclass_decision_boundary(model=model, X=X_test, y=y_test)\n","plt.show()"],"execution_count":133,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAsEAAAE/CAYAAACnwR6AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nOVIca4Q9EfxL4IaU8h/XejyKgyHU3cDKuEPjHQENnfVHPyBFTdlY9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EugpVJIbqSuwXvP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\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V8ceefDf+4jAPflFvlamogpFnB07Mtm03HONR4pEtDjuz33+N1HqQQiyJxeWke2IYi6Pj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uQdDYMwCobgf9wYIVrWKFV69/403skXWQ9/1L/SVDg/iaSDYVY+/rK6fhdTGdLBMEOvXmqZphm8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\niqIoB44KghVFURRFUZQD5/8HRDOyLMVbUCcAAAAASUVORK5CYII=\n","text/plain":["<Figure size 864x360 with 2 Axes>"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"WijzY-vDNbE9","colab_type":"text"},"source":["So far we looked at accuracy as the metric that determines our mode's level of performance. But we have several other options when it comes to  evaluation metrics.\n","\n","<div align=\"left\">\n","<img src=\"https://raw.githubusercontent.com/madewithml/images/master/basics/08_Logistic_Regression/metrics.png\" width=\"350\">\n","</div>\n","\n","<small>Image credit: \"Precisionrecall\" by Walber</small>"]},{"cell_type":"markdown","metadata":{"id":"80MwyE0yOr-k","colab_type":"text"},"source":["The metric we choose really depends on the situation.\n","positive - true, 1, tumor, issue, etc., negative - false, 0, not tumor, not issue, etc.\n","\n","$\\text{accuracy} = \\frac{TP+TN}{TP+TN+FP+FN}$ \n","\n","$\\text{recall} = \\frac{TP}{TP+FN}$ → (how many of the actual issues did I catch)\n","\n","$\\text{precision} = \\frac{TP}{TP+FP}$ → (out of all the things I said were issues, how many were actually issues)\n","\n","$F_1 = 2 * \\frac{\\text{precision }  *  \\text{ recall}}{\\text{precision } + \\text{ recall}}$\n","\n","where: \n","* TP: # of samples predicted to be positive and were actually positive\n","* TN: # of samples predicted to be negative and were actually negative\n","* FP: # of samples predicted to be positive but were actually negative\n","* FN: # of samples predicted to be negative but were actually positive"]},{"cell_type":"code","metadata":{"id":"8N8jPq_Cy2hp","colab_type":"code","outputId":"bc7f8fdc-1a91-4411-aed7-2a8efde3d6a3","executionInfo":{"status":"ok","timestamp":1583943595381,"user_tz":420,"elapsed":3932,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":459}},"source":["# Classification report\n","plot_confusion_matrix(y_true=y_test, y_pred=pred_test, classes=classes)\n","print (classification_report(y_test, pred_test))"],"execution_count":134,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAV4AAAEhCAYAAAA3X8gOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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KO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\n","text/plain":["<Figure size 432x288 with 2 Axes>"]},"metadata":{"tags":[]}},{"output_type":"stream","text":["              precision    recall  f1-score   support\n","\n","           0       0.89      0.98      0.93        58\n","           1       0.99      0.92      0.96        92\n","\n","    accuracy                           0.95       150\n","   macro avg       0.94      0.95      0.94       150\n","weighted avg       0.95      0.95      0.95       150\n","\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"9v6zc1_1PWnz","colab_type":"text"},"source":["## Inference"]},{"cell_type":"code","metadata":{"id":"kX9428-EPUzx","colab_type":"code","outputId":"b06a23c0-c41f-4415-aa5d-c624ceb4c4b4","executionInfo":{"status":"ok","timestamp":1583943595381,"user_tz":420,"elapsed":3914,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":80}},"source":["# Inputs for inference\n","X_infer = pd.DataFrame([{'leukocyte_count': 13, 'blood_pressure': 12}])\n","X_infer.head()"],"execution_count":135,"outputs":[{"output_type":"execute_result","data":{"text/html":["<div>\n","<style scoped>\n","    .dataframe tbody tr th:only-of-type {\n","        vertical-align: middle;\n","    }\n","\n","    .dataframe tbody tr th {\n","        vertical-align: top;\n","    }\n","\n","    .dataframe thead th {\n","        text-align: right;\n","    }\n","</style>\n","<table border=\"1\" class=\"dataframe\">\n","  <thead>\n","    <tr style=\"text-align: right;\">\n","      <th></th>\n","      <th>leukocyte_count</th>\n","      <th>blood_pressure</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>13</td>\n","      <td>12</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>"],"text/plain":["   leukocyte_count  blood_pressure\n","0               13              12"]},"metadata":{"tags":[]},"execution_count":135}]},{"cell_type":"code","metadata":{"id":"3qY6buxLKb2o","colab_type":"code","outputId":"6f29ad88-fd40-4260-989b-61f2308410b8","executionInfo":{"status":"ok","timestamp":1583943595382,"user_tz":420,"elapsed":3897,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Standardize\n","X_infer = X_scaler.transform(X_infer)\n","print (X_infer)"],"execution_count":136,"outputs":[{"output_type":"stream","text":["[[-0.66523095 -3.08638693]]\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"7O5PbOAvXTzF","colab_type":"code","outputId":"654640fb-5d05-4050-e04b-86ca793307d9","executionInfo":{"status":"ok","timestamp":1583943595382,"user_tz":420,"elapsed":3881,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Predict\n","y_infer = model(torch.Tensor(X_infer), apply_softmax=True)\n","prob, _class = y_infer.max(dim=1)\n","print (f\"The probability that you have a {classes[_class.detach().numpy()[0]]} tumor is {prob.detach().numpy()[0]*100.0:.0f}%\")"],"execution_count":137,"outputs":[{"output_type":"stream","text":["The probability that you have a benign tumor is 93%\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"8PLPFFP67tvL","colab_type":"text"},"source":["# Unscaled weights"]},{"cell_type":"markdown","metadata":{"id":"_XYBW85WIdKy","colab_type":"text"},"source":["Note that only X was standardized.\n","\n","$\\hat{y}_{unscaled} = b_{scaled} + \\sum_{j=1}^{k}W_{{scaled}_j}x_{{scaled}_j}$\n","* $x_{scaled} = \\frac{x_j - \\bar{x}_j}{\\sigma_j}$\n","\n","$\\hat{y}_{unscaled} = b_{scaled} + \\sum_{j=1}^{k} W_{{scaled}_j} (\\frac{x_j - \\bar{x}_j}{\\sigma_j}) $\n","\n","$\\hat{y}_{unscaled} = (b_{scaled} - \\sum_{j=1}^{k} W_{{scaled}_j}\\frac{\\bar{x}_j}{\\sigma_j}) +  \\sum_{j=1}^{k} (\\frac{W_{{scaled}_j}}{\\sigma_j})x_j$\n","\n","In the expression above, we can see the expression $\\hat{y}_{unscaled} = W_{unscaled}x + b_{unscaled} $\n","\n","* $W_{unscaled} = \\sum_{j=1}^{k} (\\frac{W_{{scaled}_j}}{\\sigma_j}) $\n","\n","* $b_{unscaled} = b_{scaled} - \\sum_{j=1}^{k} W_{{scaled}_j}\\frac{\\bar{x}_j}{\\sigma_j}$"]},{"cell_type":"code","metadata":{"id":"KTSpxbwy7ugl","colab_type":"code","outputId":"19679962-956f-4c8a-f5f0-49a4a3df31f9","executionInfo":{"status":"ok","timestamp":1583943595383,"user_tz":420,"elapsed":3850,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":68}},"source":["# Unstandardize weights \n","W = model.fc1.weight.data.numpy()\n","b = model.fc1.bias.data.numpy()\n","W_unscaled = W / X_scaler.scale_\n","b_unscaled = b - np.sum((W_unscaled * X_scaler.mean_))\n","print (W_unscaled)\n","print (b_unscaled)"],"execution_count":138,"outputs":[{"output_type":"stream","text":["[[ 0.61700419 -1.20196244]\n"," [-0.95664431  0.89996245]]\n","[ 8.913242 10.183178]\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"PbcuwPdKEMlK","colab_type":"text"},"source":["---\n","Share and discover ML projects at <a href=\"https://madewithml.com/\">Made With ML</a>.\n","\n","<div align=\"left\">\n","<a class=\"ai-header-badge\" target=\"_blank\" href=\"https://github.com/madewithml/basics\"><img src=\"https://img.shields.io/github/stars/madewithml/basics.svg?style=social&label=Star\"></a>&nbsp;\n","<a class=\"ai-header-badge\" target=\"_blank\" href=\"https://www.linkedin.com/company/madewithml\"><img src=\"https://img.shields.io/badge/style--5eba00.svg?label=LinkedIn&logo=linkedin&style=social\"></a>&nbsp;\n","<a class=\"ai-header-badge\" target=\"_blank\" href=\"https://twitter.com/madewithml\"><img src=\"https://img.shields.io/twitter/follow/madewithml.svg?label=Follow&style=social\"></a>\n","</div>\n","             "]}]}